A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In that instance, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g. comprising part of, one, or several dies) on a substrate (e.g. a silicon wafer). Transfer of the pattern is typically via imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. Known lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at one time, and so-called scanners, in which each target portion is irradiated by scanning the pattern through a radiation beam in a given direction (the “scanning”-direction) while synchronously scanning the substrate parallel or anti-parallel to this direction. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate.
Typically, the manufacturing of an integrated circuit requires that multiple patterns are applied sequentially to the substrate, whereby the multiple patterns are stacked on top of each other. When multiple patterns are thus transferred subsequently to a substrate, it may be desired to align subsequent patterns relative to each other (i.e. when a new pattern is applied, this pattern should be aligned with a pattern in a lower layer). To align a subsequent pattern to a previously transferred pattern it is important to know the location of the previously transferred pattern. In order to determine the location of a pattern on a wafer, alignment marks are transferred to predefined positions on the substrate as part of said pattern. By measuring the position of the alignment marks, information can be obtained which can be used to transfer a subsequent pattern relative to the previously transferred pattern to the substrate.
The position information of a previously transferred pattern as required for accurately transferring a subsequent pattern relative to the previously transferred pattern thus needs to be derived from the position measurements of the alignment marks. Typically, not all areas of a pattern can be used to place alignment marks; alignment marks are therefore usually placed at edges of a pattern or in so-called scribe-lanes along a circumference of a pattern. As such, the alignment mark measurements may provide in position information about the edges of the previously transferred pattern, while it is important that the center regions of the pattern used to manufacture integrated circuits are aligned with respect to each other.
To solve this, a model can be fitted to the measured positions of the alignment marks. This model can then be used to estimate the position information of a previously transferred pattern. Such position information of a previously transferred pattern (i.e. present in a lower layer) can be considered a target position for a subsequent pattern and may thus be used to accurately transfer a subsequent pattern relative to the previously transferred pattern at a desired (target) position.
Such models may e.g. be used to represent effects such as translation errors, rotation errors or magnification errors.
In order to more accurately estimate the actual position of a previously transferred pattern based on the measured positions of the alignment marks, more complex models such as higher order models are implemented as well.
The use of such higher order model may however have one or more of the following adverse effects:
Typically, a higher order model, e.g. applying higher order polynomials or basis functions may contain a comparatively large number of parameters that needs to be determined. Determining such large number of parameters requires a comparatively large number of alignment marks to be measured. This could be time consuming, thus adversely affecting the throughput of the apparatus.
The more complex the applied model and thus the more parameters that are applied, may pose a risk with respect to the accuracy of the model; a higher order model introduces a high number of degrees of freedom and may introduce parameter induced noise.